USING LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS TO GUIDE THE SEARCH FOR THE DRIVERS OF MARINE ORIGINATION AND EXTINCTION

Advances in data availability and analytical techniques have enabled work studying how global patterns of diversification have changed through deep time and what may have driven those changes. Analyses investigating these questions have taken several approaches, such as comparing empirically observed time series or through mechanistic simulations, but have yet to come to any definitive conclusions. Here we take a different approach and directly investigate the plausibility/characteristics of underlying drivers of Phanerozoic diversification patterns before testing specific hypothesized effectors.

Using fossil observations of skeletonized marine invertebrate genera from the Paleobiology Database, we use a capture-mark-recapture technique to infer time series of origination, extinction, and sampling rates (collectively called fossil time series) throughout the Phanerozoic. To investigate possible drivers of these fossil time series, we utilize linear stochastic differential equations (SDEs). SDEs can be used to model interconnected processes by including linking terms that depend on other time series. Furthermore, connections between observed and unobserved processes can be modeled, allowing searches for and characterizations of as-of-yet unidentified factors impacting observed time series. We model our fossil time series with and without unobserved underlying drivers and find that models including unobserved drivers explain diversification patterns better than those without, providing evidence for the existence of underlying drivers of marine diversification. We also characterize these unobserved drivers to the extent possible using linear SDE methods, providing mathematical clues as to the form of the discovered drivers and their variation over the Phanerozoic. We suggest that this information may be used as a guide in the search for variables affecting marine diversification; time series may be analyzed to see if they resemble or contribute to the discovered drivers. Following this, we show it is unlikely that continental fragmentation, commonly hypothesized to influence patterns of diversification, is one of the drivers we characterized.